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Robust modelling of DTARCH models

机译：DTARCH模型的鲁棒建模

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摘要

Autoregressive conditional heteroscedastic (ARCH) models and its extensions are widely used in modelling volatility in financial time series. One of the variants, the double-threshold autoregressive conditional heteroscedastic (DTARCH) model, has been proposed to model the conditional mean and the conditional variance that are piecewise linear. The DTARCH model is also useful for modelling conditional heteroscedasticity with nonlinear structures such as asymmetric cycles, jump resonance and amplitude-frequence dependence. Since asset returns often display heavy tails and outliers, it is worth studying robust DTARCH modelling without specific distribution assumption. This paper studies DTARCH structures for conditional scale instead of conditional variance. We examine L_1-estimation of the DTARCH model and derive limiting distributions for the proposed estimators. A robust portmanteau statistic based on the L_1-norm fit is constructed to test the model adequacy. This approach captures various nonlinear phenomena and stylized facts with desirable robustness. Simulations show that the L_1 -estimators are robust against innovation distributions and accurate for a moderate sample size, and the proposed test is not only robust against innovation distributions but also powerful in discriminating the delay parameters and ARCH models. It is noted that the quasi-likelihood modelling approach used in ARCH models is inappropriate to DTARCH models in the presence of outliers and heavy tail innovations.
机译：自回归条件异方差（ARCH）模型及其扩展被广泛用于对金融时间序列的波动性进行建模。提出了变体之一，双阈值自回归条件异方差（DTARCH）模型，以建模分段线性的条件均值和条件方差。 DTARCH模型还可用于对具有非对称循环，跳跃共振和幅度-频率依赖性等非线性结构的条件异方差建模。由于资产收益率经常显示出大量的尾巴和离群值，因此在没有特定分布假设的情况下，值得研究强大的DTARCH建模。本文针对条件规模而不是条件方差研究DTARCH结构。我们研究了DTARCH模型的L_1估计，并得出了所提出估计的极限分布。构建基于L_1范数拟合的稳健portmanteau统计信息，以测试模型的适当性。这种方法以理想的鲁棒性捕获各种非线性现象和风格化的事实。仿真表明，L_1估计量对创新分布具有鲁棒性，并且在中等样本量的情况下也很准确，所提出的测试不仅对创新分布具有鲁棒性，而且在区分延迟参数和ARCH模型方面也很有效。应当指出，在存在离群值和大量尾部创新的情况下，ARCH模型中使用的拟似然建模方法不适用于DTARCH模型。

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